Compressible Flow and Transonic Shock in a Diverging Nozzle

The paper is devoted to the study of compressible flows and transonic shocks in diverging nozzles in the framework of the full compressible Euler system. Consider a nozzle having a shape as a diverging truncated sector with generic opening angle: if the upstream flow at the entrance is supersonic and is near to an axial symmetric flow, and if all parameters of the upstream flow and the receiver pressure at the exit are suitably assigned, then a transonic shock appears in the nozzle. To determine the transonic shock and the flow in the nozzle leads to a free boundary value problem for a nonlinear partial differential equation. We prove that the receiver pressure can uniquely determine the location of the transonic shock, as well as the flow behind the shock. Such a conclusion was conjectured by Courant and Friedrichs, and is confirmed theoretically in this paper for the divergent nozzles. The main advantage of this paper compared with the previous studies on this subject is that the section of the nozzle is allowed to vary substantially, while the transonic shock is not assumed to pass a fixed point. The situation coincides with the requirement in Courant-Friedrichs’ conjecture. To describe the compressible flow we use the full Euler system, which is purely hyperbolic in the supersonic region and is elliptic-hyperbolic in the subsonic region. Solving the free boundary value problem of an elliptic-hyperbolic problem forms the main part of this paper. In our demonstration some new approaches, including the introduction of a pseudo-free boundary problem and the corresponding relaxation, design of a delicate double iteration scheme, are developed to overcome the difficulties caused by the divergence of the nozzle.     

Shocks in accretion flows with SPH

Summary We present the preliminary results of a time-dependent simulation, with the Smoothed-Particle Hydrodynamics tecnique, of the accretion of gas onto Schwartzschild black holes. The flow should exibit a stable shock for the parameters chosen. In the case of 1D axisymmetric simulations, we find that the predicted inner shock position is unstable. For 2D axisymmetric simulations, in the light of the first runs, we argue that in this case shocks may be a more common result.     

Interstage Pressures of a Multistage Compressor with Intercooling

This paper considers the criterion of minimum compression work to derive an expression for the interstage pressure of a multistage compressor with intercooling that includes the gas properties, pressure drops in the intercoolers, different suction gas temperatures, and isentropic efficiencies in each compression stage. The analytical expression for the interstage pressures is applied to estimate the number of compression stages and to evaluate its applicability in order to estimate interstage pressures in the operation of multistage compressors, which can be especially useful when their measurements are not available.     

Shocks in non-loaded bead chains with impurities

We numerically investigate the problem of the propagation of a shock in an horizontal non-loaded granular chain with a bead interaction force exponent varying from unity to large values. When is close to unity we observed a cross-over between a nonlinearity-dominated regime and a solitonic one, the latest being the final steady state of the propagating wave. In the case of large values of the deformation field given by the numerical simulations is completely different from the one obtained by analytical calculation. In the following we studied the interaction of these shock waves with a mass impurity placed in the bead chain. Two different physical pictures emerge whether we consider a light or a heavy impurity mass. The scatter of the shock wave with a light impurity yields damped oscillations of the impurity which then behave as a solitary wave source. Differently an heavy impurity is just shifted by the shock and the transmitted wave loses its solitonic character being fragmented into waves of decreasing amplitudes. Received 23 June 1999     

新型可压缩尺度在跨声速流动中的应用

基于von Karman长度尺度和新型Reynolds应力本构关系对k-ε湍流模型重构,将k方程封闭,采用代数形式对湍流耗散项进行模化.在KDO（kinetic dependent only）模型的基础上,引入可压缩von Karman长度尺度,得到一种适用于复杂可压缩流动的新型湍流模型CKDO（compressible kinetic dependent only）,在CKDO模型中没有任何经验系数,仅有两个来自边界层精细化标定的可调参数.对RAE2822翼型、轴对称圆筒管道凸起流动、ONERA-M6机翼跨声速流动等算例进行数值计算,结果显示CKDO湍流模型对上述算例流场的压力系数模拟结果与实验值吻合较好,表明CKDO模型能够对跨声速流场进行较为准确的模拟.      

跨音轴流压气机转子叶尖喷气扩稳机理分析

对跨音压气机Rotor35进行了多通道全三维定常/非定常叶顶喷气数值模拟。数值计算所获得实壁机匣总性能与试验结果符合良好。计算表明使用3.6%转子堵塞流量的叶顶喷气量可以获得21.4%的扩稳效果。定常计算结果显示叶顶喷气重点影响0.9叶展以上区域,使得该区域进气攻角和扩散因子减小,从而降低叶顶载荷,减小了由激波和泄漏涡相互作用形成的通道堵塞。非定常计算结果显示,叶尖喷气的扩稳效果来自两方面:一是对某一叶片叶顶的卸载作用;二是对激波/泄漏涡干扰形成的低能区重新注入轴向动量。后者对通道流通的改善作用大于前者。非常高的喷射频率使得叶顶喷气能够抑制每个通道中低速区的进一步增长,从而实现了对压气机的扩稳。     

Microscopic Shape of Shocks in a Domain Growth Model

Considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities, e.g., the inviscid Burgers equation for the simple exclusion process. The physical solutions of these partial differential equations develop discontinuities, called shocks. The microscopic structure of these shocks is of much interest and far from being well understood. We introduce a domain growth model in which we find a stationary (in time) product measure for the model, as seen from a defect tracer or second class particle, traveling with the shock. We also show that under some natural assumptions valid for a wider class of domain growth models, no other model has stationary product measure as seen from the moving defect tracer.     

Anomalous Diffusion in a Model with a Variable Percolation Radius

Anomalous diffusion models for random 1-D cluster and comb structures of length L = 100 with finite fingers and different boundary conditions are considered. The effect of electric field on anomalous diffusion is discussed. The cases with different percolation radii are compared. The comb-structure model with periodic boundary conditions is shown to be useful in studying various types of anomalous diffusion. A new diffusion type, where the average rate is higher than the typical rate, is predicted. Physical causes for this diffusion are revealed.     

Shocks and Excitation Dynamics in a Driven Diffusive Two-Channel System

We consider classical hard-core particles hopping stochastically on two parallel chains in the same or opposite directions with an inter- and intra-chain interaction. We discuss general questions concerning elementary excitations in these systems, shocks and rarefaction waves. From microscopical considerations we derive the collective velocities and shock stability conditions. The findings are confirmed by comparison to Monte Carlo data of a multi-parameter class of simple two lane driven diffusion models, which have the stationary state of a product form on a ring. Going to the hydrodynamic limit, we point out the analogy of our results to the ones known in the theory of differential equations of two conservation laws. We discuss the singularity problem and find a dissipative term that selects the physical solution.     

Magnetohydrodynamic Shocks in the Interplanetary Space: a Theoretical Review

I discuss in this brief review some properties of magnetohydrodynamic (MHD) discontinuities in the interplanetary space. My emphasis is on a special case of MHD discontinuity, namely interplanetary (IP) shocks, and those that are found at 1 AU. I derive the Rankine-Hugoniot (RH) equations to evaluate plasma parameters in the downstream region (shocked plasma) in relation to the upstream region (unshocked plasma). These properties are used to classify IP shocks in terms of their geometry and their direction of propagation in relation to the Sun. The shock geometry is determined in terms of two angles: \(\theta _{B_{n}}\), the angle between the upstream magnetic field and the shock normal, and \(\theta _{x_{n}}\), the angle between the shock normal and the Sun-Earth line. Sources of IP shocks frequently found in the solar wind at Earth’s orbit are presented. Then the RH equations are solved for two categories of IP shocks in a special case: perpendicular shocks, when \(\theta _{B_{n}}\) is 90 ^°, and oblique shocks, when that angle is 45 ^°. Finally, I highlight the importance of knowing the shock geometry, mainly the impact angle \(\theta _{x_{n}}\), specially whether the shock is frontal or inclined, for space weather-related investigations. IP shocks are known to be more geoeffective if they strike the Earth’s magnetosphere frontally, or with impact angle nearly null. These results have been reported both by modeling and experimental studies in the literature.     

On Harmonic Generation in X-Ray Free-Electron Lasers with Variable Undulator Deflection Parameter

Technical Physics - X-ray free-electron lasers (FELs) generate ultrashort bursts at wavelengths ~1 –100 Å. The possibility of harmonic generation in the X-ray range in FELs with a...     

带孔洞的金属拉伸的分子动力学

在不同负静压下对中心带有一个球形孔洞的面心立方金属铜进行分子动力学模拟,从晶体的形变,原子分布示意图,径向分布函数等方面进行讨论.发现在弱的负压下,孔洞及材料作弹性变形,超过一定阈值时出现塑性变形,并在局部出现相变.在极强的负压下,材料断裂.随拉伸应力的增加,材料经历弹性均匀拉伸——局部fcc到hcp的相变及缺陷的产生——缺陷积累产生微裂纹或空洞——材料断裂的过程.     

The DC Arc in a Supersonic Nozzle Flow

The boundary layer integral method at its second level of approximation has been used to study the DC arc in a supersonic nozzle flow. It is shown that with the inclusion of the arc momentum balance, the critical point of the flow is, generally, not the sonic point of the external flow. The speed, at which a disturbance propagates relative to the external flow, is in general supersonic and is dependent on the arc conditions. The arc model is capable of predicting the axial electric field, the arc size and the axial pressure distribution as a function of current. For affinely related nozzles, the solution is determined by a parameter N, which is related to zt, the stagnation condition and the nominal current density at the throat (I/At). Numerical results are given for a particular nozzle shape although the method of analysis is general. Practical implications as regards nozzle design for a gas blast circuit breaker are briefly discussed.     

间断Galerkin方法求解跨音压气机转子流场

本文采用间断Galerkin方法求解雷诺平均N-S方程和SA湍流模型方程,采用Roe格式计算无黏通量,混合格式求解黏性通量中的梯度。为防止跨音速流场计算中的数值振荡,采用了TVD限制器和正性修正。计算了跨音速转子NASA Rotor37在设计转速下的变工况流场,得到了与实验吻合良好的结果,表明DG方法在叶轮机械内部流动计算中具有广阔的应用前景。     

Block Elements in Contact Problems with a Variable Friction Coefficient

Contact problems on the surface interaction of rigid stamps with a deformed layered medium are considered provided that the variable friction coefficients arise in the contact zone as a function of the coordinate under the horizontal motion of stamps. The cause of the variable friction coefficients arising may be surface phenomena induced by a complex rheology of the deformed-medium surface, the chemical reactions proceeding, or a change in the properties of the contact surface of the stamps, for example, as a result of the presence of separate particles of the wear contact surface of the stamp and the base.     

Non-Ergodicity in a 1-D Particle Process with Variable Length

We present a 1-D random particle process with uniform local interaction, which displays some form of non-ergodicity, similar to contact processes, but more unexpected. Particles, enumerated by integer numbers, interact at every step of the discrete time only with their nearest neighbors. Every particle has two possible states, called minus and plus. At every time step two transformations occur. The first one turns every minus into plus with probability β independently from what happens at other places and thereby favors pluses against minuses. The second one is “impartial.” Under its action, whenever a plus is a left neighbor of a minus, both disappear with probability α independently from presence and fate of other pairs of this sort. If β is small enough by comparison with α ² and we start with “all minuses,” the minuses never die out.     

End of aging in a complex system

Aging phenomena in complex systems have been used as an important tool to investigate the physics of complexity. In particular, aging effects in spin glasses, measured using the thermoremanent magnetization decays, have been instrumental as a probe of complex equilibrium and nonequilibrium dynamics. In this Letter, we show that aging found in spin glass materials has a finite lifetime. After the aging part of the decay has ended, we find a post-aging decay which is apparently logarithmic in nature. This decay is independent of the waiting time and part of the same mechanism that produces aging.     

Calculation of Interphase Mass Transfer in a Spray Flow Produced by a Nozzle with Account of Crisis

Technical Physics - This paper describes the numerical model and the results of calculating the interphase mass transfer in a two-phase flow generated by atomizing a liquid in a gas using a nozzle....     

用于高场加速器磁体的新型高温超导内插线圈概念设计

中国科学院高能物理研究所正在进行环形正负电子对撞机-超级质子对撞机(CEPC-SPPC)的研究工作,未来超级质子对撞机(SPPC)初期要求的主环二极磁体磁场强度为12 T,升级后的磁体场强需求为20～24 T.为了达到15 T及以上的场强,高温超导线材制作的内插高场线圈是目前的唯一选择.本文对YBCO内插线圈做了相应的探究,并提出的一种新的设计方案,具有以下特点:线圈结构采用Common-coil与Block-type混合的设计,并解决了端部弯曲半径小的问题;充分利用YBCO在高场下磁场与超导带材平行时临界电流密度是垂直情况下的数倍特性,通过优化端部结构减小线材与磁场夹角;计算了不同形状及弯曲半径组合下的线材弯曲情况,综合考虑了端部长度与线材张力之间相互制约的问题,并给出了最终结果;试绕了两种端部的铜线圈,以及balloon-end的高温超导YBCO线圈并进行了测试.